CN109927035A - A kind of mapping method of multi-arm robot C- space line obstacle - Google Patents
A kind of mapping method of multi-arm robot C- space line obstacle Download PDFInfo
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Abstract
The invention discloses a kind of mapping methods of multi-arm robot C- space line obstacle, are related to robot obstacle-avoiding control field.The space C- is a kind of common barrier mapping space, barrier in working space is reduced to the models such as point, line, simplify the critical collision angle of manipulator model character pair point, line by solving, coboundary and the lower boundary of C- spatial obstacle are obtained, then barrier is obtained in the entire mapped boundaries in the space C- by their union.The present invention proposes a kind of C- space mapping method of new Eigenvector, the interference position of line segment and model is divided into four kinds of situations to discuss, it obtains corresponding mathematical model and critical collision angle method for solving, and finally summarizes the critical collision angle method for solving of any line segment in plane.The advantage of this method is to consider all interference forms of line obstacle and mechanical arm as far as possible, reduces the calculation amount that mechanical arm free space solves, avoids the collision between each joint of multi-arm robot.
Description
Technical field
The invention belongs to robot obstacle-avoiding control fields, and in particular to a kind of mapping of multi-arm robot C- space line obstacle
Method.
Background technique
Most commonly used in life and medical field at present is multi-arm robot and its system, the mechanical arm of multi-arm robot
Between can complete more complicated movement with cooperating, realize more various function.But the path of multi-arm robot is advised
It is more complicated than common tandem type industrial robot to draw control, how accurately and effectively to obtain the optimal clear path of mechanical arm
It is one of the hot spot studied at present.
The difference of robot modeling and working space description, the method for path planning is also different, but is all based on European sky
Between and two kinds of the space C- planning space carry out.Theorem in Euclid space is also referred to as robot working space, and the space-wise is normal
In the path planning of tandem type industrial robot, because each joint of industrial robot is cascaded, it is easy to pass through
Jacobian matrix realizes the conversion of cartesian coordinate system and joint coordinate system, but calculation amount is bigger.The machinery of multi-arm robot
Arm is more complicated, and other than the collision between each joint of mechanical arm itself is possible, there is also close between mechanical arm and mechanical arm
The collision of section, if, due to the presence of barrier, mechanical arm cannot reach whole poses using theorem in Euclid space method, but in C-
The obstacle pose of mechanical arm can be expressed as characteristic point, line in space, mechanical arm and characteristic point, line are collided to be formed up and down
Critical collision angle is calculated, and space with obstacle is acquired, and supplementary set is then free space.Machinery corresponding to point in free space
Arm pose will not all collide with obstacle, and this method avoid a large amount of cumbersome calculating, computational efficiencies with higher.It is logical
Cross corresponding searching algorithm, so that it may the collisionless road for connecting initial pose point and object pose point is found in free space
Diameter, with carrying out motion control according to the path.
Summary of the invention
The present invention provides a kind of multi-arm in view of the above-mentioned problems, the obstacle mapping mathematical model to the space C- is studied
Robot C-space line obstacle mapping method.Obstacle in working space is reduced to EigenvectorP 1 P 2,P 1WithP 2For line segment
Two endpoints, enable it perpendicular to X-axis, and be located at first quartile.Mechanical arm is reduced to two link mechanisms, is divided into large arm and small
Arm, wherein large arm be around the maximum distance that own axes rotateL 1, forearm is around the maximum distance that own axes rotateL 2, mechanical
Arm is around the maximum distance that its large arm own axes rotatesl max；If the centre of gyration of large arm is originO, with originOFor the center of circle,l maxFor radius, circle is doneO max, according to circleO maxWith line segmentP 1 P 2Position, four kinds of interference situation discussion can be divided into, wherein forearm return
Turn centerro 1To line segmentP 1 P 2Place straight lineMDistance bed rol ,ro 1WithP 1Distance bed rop1,ro 1WithP 2Distance bed rop2,
OriginOWithP 1Distance isd op1；Calculate separately out the critical collision angle of these four situations, so that it may obtain the line based on the space C-
Obstacle mapping space.
The first situation isP 1 P 2WithO maxThere is no intersection point, andP 1、P 2It is outer to be all located at circle, line segmentP 1 P 2C- spatial obstacle reflect
It penetrates as empty set；Second situation isP 1 P 2WithO maxThere are an intersection point, line segmentP 1 P 2C- spatial obstacle mapping, with pointP 1C- it is empty
Between obstacle mapping be same；The third situation isP 1 P 2WithO maxThere is an intersection point, andP 1Positioned at circleO maxIt is interior；4th kind of situation
It isP 1 P 2WithO maxThere is no intersection point, andP 1、P 2It is respectively positioned in circle.
Preferably, in a third case, whend op1≥L 1When, pointP 1Dyskinesia will not be caused to large arm, it only can be to small
Arm causes dyskinesia；Whend op1<L 1When, pointP 1Dyskinesia can all be caused to large arm and forearm；When large arm collides, nothing
Take what angle by forearm, robot can all collide, when large arm does not collide, forearm collide the case where withd op1≥L 1Feelings
As being concluded that under condition.
Preferably, in the fourth case, whend rol ≥L 2When, forearm will not be with line segmentP 1 P 2It collides, the space C- barrier
Hinder and is mapped as empty set；Whend rol <L 2When, forearm and line segmentP 1 P 2It collides.
Preferably, when solving the critical collision angle calculation formula of forearm, be divided into two kinds of situations: one is forearms and line segment
Endpoint collides, and second is that forearm is collided with line segment internal point, corresponds to four collision angle formulas in total；d rol Withd rop1Value influence whether forearm lower critical collision joint angle value form；d rol Withd rop2Value influence whether the upper of forearm
The value form of critical collision joint angle；When line segment to large arm constitute dyskinesia when, the lower critical impingement angle value of large arm withd op1Size it is related.
Preferably, for any line segment in planeP 1 P 2Mapping method, from originOFirst make line segmentP 1 P 2Vertical lineOH,
It sets up an officeHPolar form beH=(r OH ,θ OH ), it is then coordinately transformed, by former coordinateOXYRotate angleθ OH Newly sat
Mark, line segment will be perpendicular to X'Axis need to only be analyzed under new coordinate system and obtain critical collision joint angle, and reconvert returns former coordinate and is
It can.
Compared with prior art, the beneficial effects of the present invention are: the interference position of line obstacle and mechanical arm is divided into four kinds
Situation discussion has fully considered all possibilities of line obstacle and mechanical arm collision.When analyzing critical collision joint angle, according to
Certain rule carries out, and reduces the difficulty and calculation amount of the solution of mechanical arm free space, and final purpose is to avoid mechanical arm
Each joint collides, and is conducive to carry out the control of obstacle avoidance for robotic manipulator path planning.
Detailed description of the invention
Fig. 1 is line segment and mechanical arm collision model schematic diagram；
Fig. 2 is mechanical arm simplified model schematic diagram；
Fig. 3 is line segment and manipulator model interference position schematic diagram；
Fig. 4 a, 4b, 4c are the offline obstacle schematic diagrames of the third situation；
Fig. 5 a, 5b are the 4th kind of offline obstacle schematic diagrames of situation A1 condition；
Fig. 6 is any line segment obstacle schematic diagram.
Specific embodiment
Firstly the need of the concept for understanding critical collision joint angle, refer to being formed when connecting rod L and characteristic point P collision
Joint angle, contact the joint angle to be formed with characteristic point P when connecting rod L is rotated clockwise, referred to as upper critical collision joint angle；Connecting rod
The joint angle to be formed is contacted when L rotates counterclockwise with characteristic point P, referred to as lower critical collides joint angle.Pass through upper and lower critical collision
Joint angle can describe entire C- spatial obstacle boundary a little.
As shown in Figure 1, setting connecting rod L front end joint values it has been determined that jointJ kMotion range be [- π, π], connecting rod L and line
Section S generates collision, with two endpoints of straight lineP 1、P 2As characteristic point, situation is converted into the collision situation of connecting rod and point, one
Co-exist in four critical collision points:P 1Upper critical collision joint angleθ 1uc , lower critical collide joint angleθ 1lc ,P 2Upper critical touch
Hit joint angleθ 2uc , lower critical collide joint angleθ 2lc .It is apparent from by Fig. 1θ 1lc Actually it is not achieved, then is invalid lower critical
Collide joint angle.Similarly,θ 2uc It is also invalid.The joint angle of critical collision up and down that so connecting rod L and line segment S collide is real
On border only there are two, respectivelyθ 1uc Withθ 2lc .As can be seen that especially robot linkage is as obstacle for any barrier
When, one or several line segment can be decomposed into be analyzed, but basic principle is still mapped as with point.
Mechanical arm is reduced to two link mechanisms, is divided into large arm and forearm, it is as shown in Figure 2 to map that two-dimensional space.
Large arm is by a length ofl 1, width isw 1Rectangle and both ends semicircle composition；Forearm is by a length ofl 2, width isw 2Rectangle and one end half
Circle composition.Maximum distance is when large arm is rotated around own axesL 1=l 1+w 1/ 2, maximum distance is when forearm is rotated around own axesL 2=(l 2 2+w 2 2/4)1/2, two connecting rods can inswept maximum distance bel max=l 1+(l 1 2+w 2 2/4)1/2.For convenience of solution, it is assumed that this
Two joints can carry out the positioning of circumference any position without constraint.
Next the C- space reflection of research line segment, first discusses simplest situation.As shown in figure 3, enabling line segment perpendicular to X
Axis, and it is located at first quartile.Equipped with straight lineMIts equation indicates are as follows:M=By+C=0,C>=0,y≥0；Line segmentP 1 P 2∈M, whereinP 1=
(x,y 1),P 2=(x,y 2).Withl maxFor radius, originOFor the center of circle, circle is doneO max.According toO maxWith line segmentP 1 P 2Position, can be divided into
Following four situation, as shown in the figure.
(1) situation 1:P 1 P 2WithO maxThere is no intersection point, andP 1、P 2It is outer to be all located at circle, at this time line segmentP 1 P 2C- spatial obstacle reflect
It penetrates as empty set.
(2) situation 2:P 1 P 2WithO maxThere is an intersection point, at this point, line segmentP 1 P 2C- spatial obstacle mapping, with pointP 1C- it is empty
Between obstacle mapping be likewise, its critical collision joint angle can be acquired according to the correlation map rule of point.
(3) situation 3:P 1 P 2WithO maxThere is an intersection point, andP 1Positioned at circleO maxIt is interior.If forearm rotary centerro 1WithP 1 P 2Institute
In straight lineMDistance bed rol ,ro 1WithP 1Distance bed rop1, origin withP 1Distance isd op1(not invading inner circle).
1) whend op1≥L 1When, pointP 1Dyskinesia will not be caused to large arm, can only cause dyskinesia to forearm.
As shown in fig. 4 a, whend rol ≤L 2Andd rop1≥L 2When, forearm will not be encounteredP 1Point, forearm existθ 2uc Position andθ 2lc
Position and line segmentP 1 P 2The point collided is respectivelyA 1WithA 2。θ 1For the rotation angle value of large arm, for anyθ 1∈[θ 1min,θ 1max],
The critical collision joint angle of forearm are as follows:θ 2uc =f ol uc (θ 1,x),θ 2lc =f ol uc (θ 1,x)。
As shown in Figure 4 b, whend rol ≤ L 2Andd rop1<L 2When, lower critical collides joint angleθ 2lc , no longer it is forearm and line segment
?A 2The collision of point, becomes line segment endpointP 1With the collision of forearm coboundary.At this point, for anyθ 1∈[θ 1 ' min,θ 1 ' max],
Inθ 1 ' max=θ 1min, the critical collision joint angle of forearm isθ 2uc =f ol uc (θ 1,x),θ 2lc =f ol uc' (θ 1,x)。
2) whend op1<L 1When, pointP 1Dyskinesia can all be caused to large arm and forearm.
As illustrated in fig. 4 c, line segmentP 1 P 2The upper critical collision joint angle to be formed is collided with large arm isθ 1uc =arccos[(x-w 2/
2)/l 1]。
Lower critical collides joint angleθ 1lc Withd op1Value it is related.Whend op1∈[l 1,L 1) when, such as situation in I frame in Fig. 4 c
Shown, line segment and large arm intersect on circular arc a bitB 2, lower critical collides joint angle at this timeθ 1lc =arctan(y 1/x)-arccos
(D/2l 1 d op1), whereinD=l 1 2+d op1 2-w 1 2/4.Whend op1∈(0,l 1) when, as shown in situation in II box in Fig. 4 c, line segment with
Large arm intersects at a bit of large arm upper edgeB 3, there is lower critical to collide joint angle at this timeθ 1lc =arctan(y 1/x)-arccos(w 1/
2d op1)。
Whenθ 1∈[θ 1lc ,θ 1uc ] when, large arm collides, and no matter what angle forearm takes, and robot can all collide, institute
With line segmentP 1 P 2The C- spatial obstacle for being mapped to forearm isθ 2∈[-π,π]；Whenθ 1Not in the value of upper and lower critical collision joint angle
When in range, line segmentP 1 P 2It will cause dyskinesia to forearm, but withd op1≥L 1In the case of be concluded that it is the same.
According to circumstances 3 discussion result, it is known that originOWith pointP 1Distanced op1And originOWith pointP 2Distanced op2Length
It is short to be related to line segmentP 1 P 2Whether C- spatial obstacle is caused to large arm.
(4) situation 4:P 1 P 2WithO maxThere is no intersection point, andP 1、P 2It is respectively positioned in circle.?d op1≤L 1Ord op2≤L 1Under the conditions of,
Line segmentP 1 P 2Obstacle can all be caused to large arm and forearm, such case is previously discussed above, and is repeated no more.Next, only begging for
By line segmentP 1 P 2The case where obstacle is caused to forearm.
ro 1With straight lineMDistanced rol Withro 1With pointP 1Distanced rop1The lower critical collision joint of forearm will be influenced
The value form at angle；Similarly,d rol Withd rop2Also the value form of the upper critical collision joint angle of forearm is influenced whether.
1) whend rol ≥L 2When, forearm will not be with line segmentP 1 P 2It collides, C- spatial obstacle is mapped as empty set.
2) whend rol <L 2When, if there isd rop2≥L 2, situation is as shown in Figure 5 a, and forearm boundary will not be with pointP 2It collides,
Upper critical collision joint angle is endpointA 1Contacted with line segment generate angle andθ 2uc =f ol uc (θ 1,x)；Ifd rop2<L 2, situation is as schemed
Shown in 5b, forearm boundary existsA 3Point will be with pointP 2It collides, upper critical collision joint angleθ 2uc =f ol uc' (θ 1,x)；Ifd rop1
≥L 2When, lower critical collides joint angleθ 2lc =f ol lc (θ 1,x)；Ifd rop1<L 2When, lower critical collides joint angleθ 2lc =f ol lc' (θ 1,x)。
So far, the line segment perpendicular to X-axis is completedP 1 P 2C- space reflection, obtained it C- spatial obstacle description.
For without loss of generality, as shown in fig. 6, for any line segment in planeP 1 P 2, from originOFirst make line segmentP 1 P 2's
Vertical lineOH, the polar form for the H that sets up an office isH=(r OH ,θ OH ).It is coordinately transformed, by former coordinateOXYRotate angleθ OH , obtain newly
CoordinateO'X'Y', situation is converted to perpendicular to X'The line segment of axisP 1 'P 2 'The case where.It need to only be analyzed under new coordinate system
Critical collision joint angle out, reconvert, which returns former coordinate, (to add angleθ OH ).
Wherein, the solution formula of Partial Variable is as follows in the above scheme:
d rol It is represented byθ 1,xFunction:d rol = x-l 1cosθ 1；
P 1Polar form isP 1=(r p1,θ p1), thend rop1=[r p1 2+l 1 2-2r op1 l 1cos(θ 1-θ p1)]1/2；
P 2Polar form isP 2=(r p2,θ p2), thend rop2=[r p2 2+l 1 2-2r op2 l 1cos(θ 1-θ p2)]1/2；
Following formula is the critical angle of large arm rotationθ 1min、θ 1maxWithθ 1 ' minCalculation formula:
θ 1max=arcos [(x-L 2)/l 1] (1)
θ 1min=arcos [(l 1 2+x 2+y 1 2-L 2 2)/2l 1(x 2+y 1 2)] +arctan (y 1/x) (2)
θ 1 ' min=-arcos [(l 1 2+x 2+y 1 2-L 2 2)/2l 1(x 2+y 1 2)] +arctan (y 1/x) (3)
Following formula is the angle formula expansion of critical collision up and down generated when forearm and line segment endpoint collide:
θ 2uc =-[θ 1-arccos (d rol /d rop2)-arcsin (w 2/2d rop2)] = f ol uc' (θ 1, x) (4)
θ 2lc =-[θ 1+arccos (d rol /d rop1) +arcsin (w 2/2d rop1)] = f ol lc' (θ 1, x) (5)
Following formula is the angle formula expansion formula of critical collision up and down generated when forearm and the non-endpoint of line segment collide:
θ 2uc =-[θ 1-arccos (d rol /L 2)-arctan (w 2/2l 2)] = f ol uc (θ 1, x) (6)
θ 2lc =-[θ 1+arccos (d rol /L 2) +arctan (w 2/2l 2)] = f ol lc (θ 1, x) (7)
Above-mentioned formula is acquired according to corresponding mathematical model.
The foregoing is merely specific embodiment of the present invention, those skilled in the art are in skill of the present invention
The replacement carried out in art aspects should be all included within protection scope of the present invention.
Claims (5)
1. a kind of mapping method of multi-arm robot C- space line obstacle, it is characterized in that: the obstacle in working space is reduced to
EigenvectorP 1 P 2,P 1WithP 2It for two endpoints of line segment, enables it perpendicular to X-axis, and is located at first quartile；Mechanical arm is simplified
For two link mechanisms, it is divided into large arm and forearm, wherein large arm is around the maximum distance that own axes rotateL 1, forearm is around itself axis
Line rotation maximum distance beL 2, mechanical arm is around the maximum distance that its large arm own axes rotatesl max；If in the revolution of large arm
The heart is originO, with originOFor the center of circle,l maxFor radius, circle is doneO max, according to circleO maxWith line segmentP 1 P 2Position, four kinds can be divided into
Interfere situation discussion, wherein forearm rotary centerro 1To line segmentP 1 P 2Place straight lineMDistance bed rol ,ro 1WithP 1Distance bed rop1,ro 1WithP 2Distance bed rop2, originOWithP 1Distance isd op1；The critical collision angle of these four situations is calculated separately out, just
The available line obstacle mapping space based on the space C-；
The first situation isP 1 P 2WithO maxThere is no intersection point, andP 1、P 2It is outer to be all located at circle, line segmentP 1 P 2C- spatial obstacle be mapped as
Empty set；Second situation isP 1 P 2WithO maxThere are an intersection point, line segmentP 1 P 2C- spatial obstacle mapping, with pointP 1The space C- barrier
It is same for hindering mapping；The third situation isP 1 P 2WithO maxThere is an intersection point, andP 1Positioned at circleO maxIt is interior；4th kind of situation beP 1 P 2
WithO maxThere is no intersection point, andP 1、P 2It is respectively positioned in circle.
2. a kind of mapping method of multi-arm robot C- space line obstacle as described in claim 1, it is characterized in that: in the third feelings
Under condition, whend op1≥L 1When, pointP 1Dyskinesia will not be caused to large arm, can only cause dyskinesia to forearm；Whend op1<L 1When,
PointP 1Dyskinesia can all be caused to large arm and forearm；When large arm collides, no matter what angle forearm takes, and robot all can
Collide, when large arm does not collide, forearm collide the case where withd op1≥L 1In the case of be concluded that it is the same.
3. a kind of mapping method of multi-arm robot C- space line obstacle as described in claim 1, it is characterized in that: in the 4th kind of feelings
Under condition, whend rol ≥L 2When, forearm will not be with line segmentP 1 P 2It collides, C- spatial obstacle is mapped as empty set；Whend rol <L 2When, it is small
Arm and line segmentP 1 P 2It collides.
4. a kind of mapping method of multi-arm robot C- space line obstacle as described in claim 1, it is characterized in that: solving forearm
Critical collision angle calculation formula when, be divided into two kinds of situations: one is forearms and line segment endpoint to collide, and second is forearm
It is collided with line segment internal point, corresponds to four collision angle formulas in total；d rol Withd rop1Value influence whether to face under forearm
The value form of boundary's collision joint angle；d rol Withd rop2Value influence whether forearm upper critical collision joint angle value form；
When line segment to large arm constitute dyskinesia when, the lower critical impingement angle value of large arm withd op1Size it is related.
5. a kind of mapping method of multi-arm robot C- space line obstacle as described in claim 1, it is characterized in that: in plane
Any line segmentP 1 P 2Mapping method, from originOFirst make line segmentP 1 P 2Vertical lineOH, set up an officeHPolar form beH=(r OH ,θ OH ), it is then coordinately transformed, by former coordinateOXYRotate angleθ OH New coordinate is obtained, line segment will be perpendicular to X'Axis only needs
Analysis obtains critical collision joint angle under new coordinate system, and reconvert returns former coordinate.
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